Fractons, geometrically

Angus, Stephen; Kim, Minkyoo; Park, Jeong-Hyuck

doi:10.48550/arxiv.2111.07947

Cited by 4 publications

(4 citation statements)

References 89 publications

(129 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• It would be interesting to explore how the current formulation is related to other geometric constructions [64][65][66] as well as the associated interplay with gravitational physics.…”

Section: Summary and Discussionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono¹,

You²,

Angus³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the 't Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions. CONTENTSI. Introduction II. Fractons from nonuniform higher-form symmetries A. Nonuniform higher-form symmetries B. Strategy to realize fractons C. Deformation of symmetry generators III. Gauge theory with U (1) and dipole symmetries A. U (1) and dipole symmetries and their gauging B. Gauge theory of U (1) charge-and dipole-gauge fields C. Low energy limit and the relation to the scalar charge gauge theory D. Number of gapless modes E. Higher-form symmetries and fractons F. Dual theory G. SSB of higher-form symmetries H. Extended operators at low energies I. Gauging of nonuniform higher-form symmetries, 't Hooft anomalies, and an SPT action J. Higgsing and fracton order K. Variants of the scalar charge gauge theory IV. Vector charge gauge theory from nonuniform symmetries

show abstract

“…• It would be interesting to explore how the current formulation is related to other geometric constructions [64][65][66] as well as the associated interplay with gravitational physics.…”

Section: Summary and Discussionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono¹,

You²,

Angus³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The present work opens various avenues for further research. One is the generalization of this analysis to other interesting models like the traceless scalar charge theory, their vector generalizations and beyond, see, e.g., [17,18,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Another possiblity is to allow for curved space(-time) [19,25,54].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Asymptotic symmetries and soft charges of fractons

Pérez¹,

Prohazka²

2022

Preprint

View full text Add to dashboard Cite

The asymptotic structure of gauge theories describing fracton interactions is analyzed. Two sets of asymptotic conditions are proposed. Both encompass all known solutions, lead to finite charges and resolve the problem of the divergent energy coming from the monopole contribution. While the first set leads to the expected fracton symmetry algebra, including a dipole charge, the second set provides a soft infinite-dimensional extension of it. These soft charges provide evidence of a rich infrared structure for fracton-like theories and provide one corner of a possible fracton infrared triangle.

show abstract

“…Recently, HRS has attracted much attention from fields other than condensed matter physics, see, e.g., Refs. [33][34][35][36][37]. It is also interesting to ask the questions about defects.…”

mentioning

confidence: 99%

Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids

Yuan¹,

Chen²,

Ye³

2022

Preprint

View full text Add to dashboard Cite

Along the line of Phys. Rev. Research 2, 023267 (2020), Phys. Rev. Research 3, 013226 (2021) and Phys. Rev. Research 3, 043176 (2021), in this work we develop the theory of symmetry defects of higher-rank continuous symmetry (HRS) in spontaneously HRS breaking phases dubbed fractonic superfluids. According to Noether's theorem, HRS is associated with the conservation law of higher moments, e.g., dipoles, quadrupoles, and angular moments. The familiar vortices in 2D conventional superfluid thin film are identified as defects of rank-0 U (1) symmetry that is associated with particle number conservation. We start with a fractonic superfluid with angular moment conservation. We establish configurations of defects. Then, we construct bound states of symmetry defects, which have finite excited energy. By using bound states, we study the physical consequence of proliferation of symmetry defects, which leads to a hierarchical structure of defect proliferation. Various scenarios of Kosterlitz-Thouless-type topological transitions driven by higher-rank defects are discussed.

show abstract

Fractons, geometrically

Cited by 4 publications

References 89 publications

A symmetry principle for gauge theories with fractons

A symmetry principle for gauge theories with fractons

Asymptotic symmetries and soft charges of fractons

Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids

Contact Info

Product

Resources

About